What are the pros and cons with using the Blender installed Python or the system Python?
Opining on the pros of both.
Possibly walking a fine line re being closed as an opinion based question, more suitable for a forum
As I see it, the big &quot;PRO&quot; for the bundled python lies with the distributors and non python minded users of Blender. A Blender version is built against a certain version of python, and will only run when the x.y of the python x.y.z version (built against vs run against) match. Blender could distribute blender without a bundled python, and inform which version to install. Rather than doing this they have included a bare bones install of the required version.
As intimated in question, the big &quot;PRO&quot; of using  a system based python is it is often a lot easier to install 3rd party modules using the OS's package manager, and to get help if and when there are issues.
Recall numpy being an example of this. Once upon a time the python bundled with blender came without numpy.  As scripts and addons began to appear using numpy, so did questions of &quot;cant install numpy to use with blender&quot;,  &quot;blender can't see my numpy&quot;... Now numpy comes pre installed as a site package of the bundled python.  The end user can now use the script / addon and be blissfully unaware of pip n PYTHON_PATH's and all that other &quot;fun&quot; stuff.  Perhaps PIL may get in.